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An Eaton-Kortum Model of Trade and Growth

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One of the remarkable features of the Eaton-Kortum model is that it allows us to estimate the effects of trade liberalization on the extended trade margins (i.e. the numbers or fractions of varieties that each country imports from and exports to other countries). analyze. levels of asymmetry across countries.2 However, their static formulation misses the fact that countries tend to export more and more varieties as they grow faster than the rest of the world (e.g. Hummels and Klenow, 2005; Kehoe and Ruhl, 2013). Allowing for different growth paths across countries can help explain the evolution of the expanded margins that the static framework cannot describe.3 The purpose of this paper is to develop an Eaton-Kortum model of trade and growth. developed to examine how trade liberalization affects countries' growth rates and expanded trade margins over time. As this lowers the country's rate of return to capital, its growth rate tends to fall back.

Because this increases the relative rents and thus the terms of trade of countries 2 and 3 relative to country 1 via the above-mentioned stabilization mechanism, all countries grow at a higher balanced growth rate in the long run. Country 1's unilateral trade liberalization for imports from country 2 shifts its extensive import margins from country 3 to country 2. Not only that, it also increases country 1's extensive export margins to all destinations due to lower long-term rental prices. to countries 2 and 3.

The last result implies that country 3's return to capital, and thus its welfare, falls in the static Eaton–Kortum model. In our dynamic model, however, even country 3's total welfare can increase through accelerated long-term growth. This means that the growth rate in the country is falling inτnjrj/rn. This makes intuitive sense: a decrease iτnj or an increase inrn/rj, the latter indicating an improvement in country n's terms of trade p(in)/p(ij) = (rn/rj)an(in)/aj(ij), raises its growth rate.

This would make the long-run effects of trade liberalization different from the short-run effects consistent with the static Eaton-Kortum model.

Fractions of domestic and traded varieties

This is a very powerful result: regardless of the signs and magnitudes of a∗12 and a∗21, trade liberalization anywhere does increase the balanced growth rate. This is because trade liberalization in one country not only increases its own growth potential, but also increases the terms of trade of the other countries vis-à-vis the liberalizing country. For example, a fall inτ12laerr1∗, which raises the terms of trade of country 3 vis-à-vis country 1.

These improvements in the terms of trade for the non-liberalizing countries contribute to the higher balanced growth rate. This statement implies that the positive long-term effect of the unilateral trade liberalization in Naito (2012) still holds in a three-country case, although we will see in section 3.3 that this may not be true in the short run for some countries. Although you may be disappointed that we find the directions of changes in only four of the nine fractions of varieties, this statement actually has rich implications.

First, in country 1, some varieties imported from country 3 are substituted by those imported from country 2. This is because the fall in τ12 makes the latter varieties cheaper than the former for the liberalized country. For country 2 or 3, the declines in r1∗andr1∗/r∗2 caused by the decline in τ12 make it cheaper to import varieties from country 1 than from other sources.

This proposition is stronger than the previous one in the sense that the directions of changes in all nine variety fractions are unambiguously determined under bilateral trade liberalization, with bilateral trade terms remaining unchanged in the long run. In fact, Proposition 3 can be seen as just a composite of Proposition 2 applied to τ12 and τ21: a preferential trade agreement between countries 1 and 2 shifts their import requirements from the outsider to any insider, and also increases their fractions of exported varieties. to both indoor and outdoor destinations. This indicates that the preferential trade agreement induces trade creation (i.e., π11∗ andπ∗22 are replaced by π∗12 andπ∗21, respectively) and trade diversion (i.e., π13∗ andπ∗23 are replaced byπ12∗ andπ∗21). ,respectively).

Finally, the fact that country 3's fractions of exported varieties decrease does not mean that the non-member country loses out on the preferential trade agreement. It actually enjoys the highest balanced growth rate along with improved terms of trade vis-à-vis both countries 1 and 2.

Comparison with short-run effects

In contrast to unilateral trade liberalization, bilateral trade liberalization, which leaves bilateral trade terms unchanged in the long run, increases not only r2 but also r1 in the short run. Due to the strong direct effects of the declines in τ12 and τ21, both trade creation and diversion occur even in the short term. The gaps in the short-term growth rates pull both r1 and r2 down below their old BGP values, which in turn increases the balanced growth rate.

As country 3's varieties become relatively more expensive, country 3 imports more from both countries 1 and 2 in the long run. Proposition 4 Based on the symmetric BGP, both trade liberalization schemes specified in Propositions 2 and 3 raise γ1 and γ2, but lower γ3 in the initial period. As long as we are around the symmetric BGP, trade liberalization, whether unilateral or bilateral, must lower the growth rate of a non-liberalizing country (ie, country 3) in the short run.

In the two-country model of Naito (2012), a fall inτ12 improves the terms of trade of country 2 vis-à-vis country 1, which in turn increases the growth rate in country 2 in the initial period. It is true that a fall inτ12 still improves country 2's terms of trade vis-à-vis all other countries, even in our three-country model, thereby boosting country 2's growth rate in the short run. This fact, however, implies that country 3's terms of trade vis-à-vis country 2 must deteriorate, reducing country 3's growth rate in the short term.

The fact that the initial growth rate in country 3 falls from its old BGP value in our model means that r3/pY3 and thus the welfare of country 3 must fall in the static model. Conversely, the rise in the equilibrium growth rate in our model caused by liberalization can increase the overall utility of country 3, reversing the pessimistic view from the static Eaton-Kortum model. The simulated values ​​of rents and shares of varieties in the short and long term as a result of unilateral and bilateral trade liberalization are also unchanged.

Third, the difference between the short- and long-term effects of trade liberalization opens the possibility that its welfare effects can be reversed in a positive direction in the static Eaton-Kortum model. According to the standard optimal tariff argument, a decline in a country's import tariffs will reduce short-term welfare in part through lower tariff revenues associated with deteriorating terms of trade. But since the tariff reduction increases the equilibrium growth rate, as does a decrease in the iceberg's corresponding trade costs, the liberalizing country's welfare partially increases in the long run.

We first examine the directions of changes in the long-run fractions of varieties not covered in Proposition 2. The last inequality means that, around the symmetric BGP, a fall inτ12 indeed lowers γ3 in the short run. Contrary to its long-run effects, bilateral trade liberalization increases both r1 and r2, with r1/r2 unchanged even in the short run.

Due to the worsening terms of trade for countries 1 and 2, their growth advantages over country 3 will disappear in the long run.

Fig. 1. Paths of main endogenous variables under unilateral trade liberalization in the calibrated case.
Fig. 1. Paths of main endogenous variables under unilateral trade liberalization in the calibrated case.

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